Though supporters rolled out a final version of the bill last week to try to win over more GOP senators, conservatives, led by Cotton and Kennedy, are expected to get votes on three amendments.

Cotton, in a National Review op-ed published Monday, said his potential changes would help "limit the damage" and conservatives who had already said they would support the bill "have jumped on the bandwagon too soon."

"A number of serious felonies, including violent crimes, are still eligible for early release in the version of the bill the Senate will vote on in a matter of days. In short, the First Step Act flunks their basic test to protect public safety," Cotton wrote.

He added in a separate tweet that opponents to his amendments were circulating false claims about his proposed changes.

Cotton and Kennedy’s changes would including requiring that the victims or families of victims are notified when an individual is released. Another change would be to make publicly available rearrest data for those released, as well as information on prior offenses by those released and the crimes for which they were imprisoned.

The Kennedy-Cotton amendments would also add approximately 10 offenses to a list that excludes someone from being eligible for the bill’s earned-time credits, which could be used to shorten sentences.

Toomey said in a statement that he was still weighing supporting the bill but voted no on Monday because it will block senators from voting on an amendment that he wanted to offer.

“The First Step Act contains worthwhile provisions that seek to improve the criminal justice system and reduce offender recidivism, which is why I am seriously considering supporting it. However, today’s procedural vote was designed to preclude amendments, including one I intended to offer to support victims of crime," Toomey said.

The amendment votes are expected to be held with a simple majority threshold, meaning at least a few GOP senators would need to join with all Democrats to block them from getting added to the bill.

"The amendments that he will propose tomorrow, the senator from Arkansas, have been opposed by groups across the board, left and right, conservative, progressive, Republican, Democrat, they all oppose his amendments. ... If he goes with the amendments we've seen, we're going to have to do our best to oppose him," Durbin said.